LOGIC

Dr.BCR.Mangala pirya
Wat suthivararam
sathorn,yannawa
Bangkok,10120.
thailand

Logic

- The science of reasoning
- The science that evaluates arguments
- The study of the methods and principles use to distinguish good (correct) from bad (incorrect) reasoning.

Reasoning is a special kind of thinking I which problems are solved, in which inference takes place, that is, in which conclusions are drawn from premises.

Inference
An inference is the process by which one proposition is arrived at and affirmed on the basis of one or more other propositions accepted as the starting point of the process.
An inference is the reasoning process expressed by an argument.
Inferences may be expressed through conditioned statements as well.

Argument
An argument is a group of proposition, one of which (the conclusion) is claimed to the supported by the others (the premises).

Premises

Argument

Conclusion



Proposition
Premises Evidence / Reason
Proposition


Conclusion Proposition what is claimed to follow
from the evidences.


Premise and Conclusion

Premises are the propositions which are the reasons given I support of an argument’s conclusion.
The Conclusion is the proposition that is affirmed or supported on the basis of the other propositions of the argument.

Proposition / Statement

A proposition is what a declarative sentence is typically used to assent.
A proposition is a sentence that is either true or false in other words, typically a declarative sentence.

Parts of Argument

Premise (s) + Conclusion : Argument



Whether a proposition is a premise a conclusion is determined by how it is used, not by where it happens to occur I the passage.
It is possible to express the very same argument in a number of ways :
1) Since Marie is a logic student, and since all logic students are bright, Marie must be bright.
2) Marie must be bright. After all, she is a logic student, and we know that all logic students are bright.
3) It follows logically that because Marie is a logic student she must be bright, since all logic students are bright.

Recognizing Arguments

The best way to recognize arguments is form context.
A passage is an argument if its purpose is to prove or show that something is true by offering evidence in its support.
Phrases or terms like it follows that, since, and so we must conclude that strongly suggest the presence of an argument
“If both Saturn and Uranus have sings, them Saturn has
sings”

This passage is a conditional proposition but not an argument because its antecedent is not claimed to be true.
Both Saturn and Uranus have sings.
Therefore, Saturn has sings.
This passage is an argument because its premise is claimed to be true and intended to prove that its conclusion is true (not why it is so).

Deductive and Inductive Arguments
Deduction is necessary or certain reasoning. A deductive argument is one whose conclusion is claimed to follow its premises with logical certainty.
“Because all humans are vertebrates and Smith is a human, therefore Smith is a vertebrate”.
The conclusion must follow; the premises logically entail, or guarantee it. The very meaning of the premises makes the conclusion logically necessary.
A deductive argument is valid if and only if it is not possible for all of its premises to be true and its conclusion false.
An inductive argument is one whose conclusion is claimed to be more or less probable but not certain.
Induction is probable reasoning.
In an inductive argument, the conduction is likely or probable but never logically certain.
“Employee Brown has arrived on time for work the last thousand days. Therefore, he’ll probably arrive on time today.”
There’s nothing certain about this conclusion. Brown may be ill a have had an accident or have overslept.

Signal ~ indicator words of the conclusion

So, thus, therefore, consequently, it follows that, as a result, hence, finally, in conclusion, and the like.

Signal words of the premise
Since, as, because, for, in as much as, for the reason that, and the like.

Signal words of deductive arguments
Necessary, certainly, absolutely, definitely, and the like.

Signal words of inductive arguments
Probable, improbable, plausible, implausible, likely, unlikely, reasonable to conclude, and the like.

Categorical Proposition

All subject are predicate
No term are not term

Some

Quantifier copula




Affirmative Negative
A: All S are P E : No S are P
All humans are No humans are
mortal mortal



I : Some S are P D : Some S are not P
Some human are Some humans are
mortal. not mortal.


Universal





Particular





S
P
S
P
All S are P
No S are P














Some S are P


X
S
S
P





Some S are not P
X
P
Conversion



S P S P




No S are P No P are S




S P S P
X X



Some S are P Some P are S





S P S P




All S are P All P are S




S P S P
X X



Some S are not Some P are not S

Obversion



S P S P




All S are P No S are non P
(There are no S outside P circle)



S P S P




No S are P All S are non P
(All S are outside P circle)



S P S P
X X



Some S are P Some S are not non P
(Some S are not outside P circle)




S P S P X X
Some S are not P Some S are non P
Contraposition



S P S P




All S are P All non P are non S









S P S P
X X


Some S are not P Some non P are not non S


















Standard Form of a Syllogism

1. Quantifier + Subject + Copula + Predicate
Major Premise
(Contains major term & middle term)

2. Quantifier + Subject + Copula + Predicate
Minor Premise
(Contains minor term & middle term)

3. Quantifier + Subject + Copula + Predicate


minor term major term
conclusion


Rules for Categorical Syllogisms

Another method of proving the validity of syllogisms and syllogism forms is to use five rules stating properties that all valid syllogisms must possess. A syllogism that violates any one of these rules is invalid.
1) A middle term that is distributed at least once/.
2) No term distributed in the conclusion that is not distributed in a premise.
3) At least one affirmative premise.
4) A negative conclusion if one of its premises is negative, and a negative premise if the conclusion is negative.
5) One particular premise if the conclusion in particular.


Proposition
Subject Term
Predicate Term
A
E
I
O
Distributed
”
Undistributed
”
Undistributed
Distributed
Undistributed
Distributed

เริ่ม Logic 2



Rule 1

The middle term must be distributed at least once.
All cats are animals.
All dogs are animals.
So : All dogs are cats.
In this syllogism, the middle term “animals” in both premises occurs as the predicate of an A Proposition and therefore, is not distributed in either premise. The reason of this rule is that the major premise is not speaking about every animal, so we don’t know whether the particular ones spoken about in the minor premise are the same ones spoken about I the major premise.

Rule 2

If a term is distributed in the conclusion, then it must be distributed in a premise.
All horses are animals
Some dogs are not horses.
So : Some dogs are not animals.
In this syllogism, the major term, “animals”, is distributed in the conclusion but not in the major premise, so the syllogism violates the second rule of validity.
All tigers are mammals.
All mammals are animals.
So : All animals are tigers.
In this example, the minor term, “animals”, is distributed I the conclusion but not in the minor premise. The conclusion …… the premises, saying more than the evidence allows.

Rule 1

Animals

Cats

Dogs












Classes of cats and dogs can relate to different parts of the class of animals.


Rule 2

Animal
Mammal


Tiger



The circle of “tiger” is just a part of the circle of “animal”. The circle of “animal” has other parts which are not “tigers”. So we cannot conclude that “All animals are tigers.”Rule 3

In a valid syllogism, these must be at least one affirmative premise, that is, two negative premises are not allowed.

Some females are not mothers.
Some politicians are not females.
So : Some politicians are not mothers.

In this syllogism, both premises are negative, and, therefore, the syllogism violates this rule. The reason for this rule is that the subject and the predicate terms of the conclusion share no basic for a relationship. In the example, the subject, politicians, and the predicate, mothers, are excluding form their classes the middle term, females. As a result, the premises allow us no way to relate the classes mothers and politicians as the conclusion attempts to do.

Rule 3




Mother Female Politicians



Or



Mother Female


Politicians



Since both premises are negative, the three terms are not related. So we don’t know whether the terms in the conclusion are related or not because both the major term and the minor term are not related to the middle term.

Rule 4

A negative premise requires a negative conclusion, and negative conclusion requires a negative premise. In other words, if either premise of a syllogism is negative, its conclusion must be negative.
All crows birds.
Some wolves are not crows.
So : Some wolves are birds.
This syllogism draws an affirmative conclusion from a negative premise, so it is invalid.
All honest persons are good men.
Some students are honest persons.
So : Some students are not good persons.
This syllogism draws a negative conclusion from affirmative premises.
So if a conclusion is affirmative, both premises must be affirmative and if a conclusion is negative, one premise must be negative.

Rule 4

bird

Bird

Crow Wolf or Crow Wolf




Since the minor premise negates the relationship between “wolf” and “crow”, there is no basis for the relationship between “wolf” and “bird”. So we can’t conclude that some wolves are birds; we can conclude only that some wolves are not birds.



Good men
Good men

honest
Honest Student or person Student
Person





Since the premise state only the relationship between these term, we don’t know the other parts of “student” which are not related to “honest person”. (they may be either related to good men or not.)

Rule 5
No valid syllogism has two universal premises and a particular conclusion. In other words, if both premises are universal the conclusion cannot the particular.
No lawbreakers are good citizens.
All speeders are lawbreakers.
So : Some speeders are not good citizens.

This syllogism draws a particular proposition from universal propositions. It’s invalid because the conclusion makes an existential claim that its premises just do not allow; the conclusion states that there exists at least one speeder, but the premises don’t contain any such implication, i.e. universal propositions do not state that there exists at least one lawbreakers and that there exists at least one speeder.

Exercise

Identify the rule that the following syllogisms violate :
1) All mothers are females.
Some students are females.
So : Some students are mothers.

2) All doctors are college graduates.
Some doctors are not golfers.
So : Some golfers are not college graduates.

3) All mammals are animals.
All unicorns are mammals.
So : Some unicorns are animals.

4) No mothers are males.
Some males are politicians.
So : Some politicians are mothers.

5) No fish are mammals.
Some dogs are not fish.
So : Some dogs are not mammals.


A

1

2 4
3
B C
5 6 7


















(1) Some M are P.
(2) All S are M.
(3) So : Some S are P.


M




4
3 X
S P






After diagramming the universal premise (2), it is still not clear where to place an X either in 3 or in 4. So we have to place the X on the line that separates the two parts (3 and 4). The conclusion states that there is an in the area where the S and P circles overlap. Inspection of the diagram reveals that the single is dangling outside of this overlap area. We do know if it is in or out. Thus the syllogism is invalid.


(1) All Greeks are mortals.
(2) No humans are Greeks.
(3) So : No humans are not mortals.

(1) + (2)
G








H M


But (3)

G









H M

So in diagramming the premises of this syllogism, we have not also diagrammed its conclusion.

(1) Some professors are easy graders.
(2) All professors are teachers.
(3) So : Some teachers are easy graders.

P



X

T E

In diagramming (1), it becomes clear that we have to place an X in area 3 not 4 after shading in for (2).
The conclusion (3) states that there is an X in the area where the T and the E circles overlap. Inspection of the diagram reveals that there is indeed an “X” in this area, so the syllogism is valid.

(1) All warriors are heroes.
(2) Some Greeks are not warriors.
(3) So : Some Greeks are not heroes.

W






G 5 X 6 H


If this syllogism were valid, then in diagramming its premises, we would have placed an X either in area 5 or in area 6. But no X has been placed either in 5 or in 6, for the X was placed on the live between 5 and 6. So we cannot guarantee the truth of the conclusion on the basis of the evidence afforded by its premises, and hence the syllogism in invalid.

No astronauts are Buddhist.
Some vegetarians are Buddhists.
Therefore, some vegetarians are not astronauts.
B



X

V A




Enthymemes

An enthymeme is an argument that is expressible as a categorical syllogism but in which a premise or conclusion is missing.
Examples : “Politicians are bad because they are selfish”.
This enthymeme omits as is missing the premise “All selfish people are bad”. Translating this entire argument into categorical form, we have,
All selfish people are bad people.
All politicians are selfish people.
So : All politicians are bad people.

“Animals that are loved by someone should not be sold to a medical laboratory, and lost pets are certainly loved by someone”.

This enthymeme is missing the conclusion “Lost pets should not be sold to a medical laboratory”.
How to form a syllogism from an enthymeme

1) Spit the enthymeme into 2 propositions
2) Determine what is missing, whether premise or conclusion.
3) Determine what are 2 terms that occur just once in the enthymeme.
4) Rebuild the missing proposition by using the remaining terms.
5) Translate the entire argument into categorical form.

In converting enthymemes into syllogisms, we must introduce the omitted proposition with the aim of converting the enthymemes into valid arguments.

An example of converting an enthymeme into a syllogism :

Venus completes its orbit in less time than the Earth, because Venus is closes to the sun.

Missing premise : Any planet closer to the sun completes its orbit in less time than the Earth.

Translating this argument into categorical form, we have,
All planets, closer to the sun are planets the complete their orbit in less time than the Earth.
All planets identical to Venus are planets closer to the sun.
So : All planets identical to Venus are planets that complete their orbit in less time than the Earth.

In some cases like ads, an enthymeme may be missing its premise and conclusion. For e.g.,

Star athletes drink milk.
The purpose of such a message is to persuade us to buy and drink milk. Its implied conclusion would have us do something : “Milk is a liquid you should drink”. And its missing premise is “A liquid that star athletes drink is a liquid that you should drink”. After completing the whole argument, we get (a liquid that star athletes drink is a liquid that you should drink.)
Milk is a liquid that star athletes drink.
(Milk is a liquid you should drink.)

However, this ad enthymeme is rather absurd, because it does not state the real reason why you and even star athletes should drink milk.

Exercise

Supply the missing proposition
1) Some books are thrillers; so some thrillers must be mysteries.
2) Diamond is expensive, because it is rare.
3) The Thais are charitable because they are Buddhists.
4) Born a man, you should live a blameless life.
5) Not all chardonnays are good wines. But all of them are expensive.

SORITES

A sorites is a chain of categorical syllogisms in which the intermediate conclusions have been left out. We can consider it to be an enthymematic version of a chain of the syllogisms. Example :
1) All animals are life forms.
2) All insects are animals.
3) All bees are insects.
4) So : All been are life forms.

This is a chain of two valid syllogisms. The first two premises validly imply the intermediate conclusion “All insects are life forms”. Here, the first syllogism is as follows:
All animals are life forms.
All insects are animals.
So : All insects are life forms.

And then we use the conclusion of his syllogism and the third premise of our original argument as premises of the second valid syllogism.
All insects are life forms.
All bees are insects.
So : All bees are life forms.

When these two syllogisms are valid, this sorites is also valid.
Sorites can have as many premises as you wish. Here is one with four premises :
All musicians are entertainers.
All bass players are musicians.
Some lead singers are bass players.
No rockets scientists are entertainers.
So : Some lead singers are no rocket scientists.
This sorites can be broken down into valid syllogisms.

Exercise

Supply the intermediate conclusions.
1) All bloodhounds are dogs.
All dogs are mammals.
No fish are mammals.
No fish are bloodhounds.

2) No one who studies logic is stupid.
Anyone who is dull makes a bad writer.
Stupid persons are dull.
No one who studies logic makes a bad writer.


Arguments Containing Compound Propositions

They are many arguments containing compound propositions of a special kind, and they depend for their validity upon the special properties of these propositions.

Conditional Propositions

There are two valid forms of arguments containing conditional propositions :

Modus ponens
If p then q
p
so : g

e.g. If it rains, then the road will be wet.
It rains.
Therefore, the road will be wet.

Modus Tollens

If p then q
Not g
So : not p

e.g. If it rains, the road will be wet.
The road is not wet.
So : It does not rain.

Chain Argument (or hypothetical syllogism)

It is another kind of the valid form consisting of three conditional propositions, the consequent of the first being the same as the antecedent of the second :
If p then g e.g. If it mains, the road will be wet.
If g then r If the road is wet, traffic will be heavy.
So : if p then r So : If it rains, traffic will be heavy.


Disjunctive Syllogism
(Either) A or q
Not p
So : q

e.g. This is a wasp, or this is a spider.
This is not a wasp.
So : this is a spider.


(Either) p or q
Not q
So : p


e.g. This is a wasp, or this is a spider.
This is not a spider.
So : This is a wasp.

Conjunctive Arguments

The following are two valid forms of conjunctive arguments :

Not (p and q) e.g. Sue and Kim don’t both smoke.
P Sue smokes.
So : not q So : Kim doesn’t smoke.

Not (p and q) e.g. Jon and Tim aren’t both poor.
q Tim is poor.
So : not p So : Jon isn’t poor.

Four factors in determining the reliability of a generalization :
1) Comprehensiveness : the sample is comprehensive of the group. If must not overlook the many subgroups within the group.

2) Size : the more instances observed, the more reliable the generalization. The size of any sample is tied directly so the size of the group and the member of subgroups within it.

3) Randomness : each member of the group has an equal chance of ending up as part of the sample. For e.g. we cannot sample only the tomatoes on the top because not every tomato had an equal chance of being picked.

4) Margin for Error : This deals with the breadth of the claim made by any generalizations. The greater the margin for error, the more reliable is the generalization.

Categorical inductive generalization
(induction by enumeration)

All examined copper things conducts electricity.
So : All copper things conduct electricity.

The beams in the observed sample are grade A.
Therefore, the beans in the barrel are grade A.




Several basketball players are taller than 6 feet.
Therefore, most basketball players are taller than 6 feet.

Statistical inductive generalization

Twenty percent of the birds I have seen today were robins.
So : twenty percent of the birds now in my mart of the country are robins.
80 percent of all the beans in the sample drawn are grade A.
So : 80 percent of all the beans in the barrel are grade A.
Half of the tosses of this coin observed so far have landed heads up.
So : half of the tosses of the loin will land heads up.

Inductive Analogy
An argument from analogy is an inductive argument in which a known similarity that two things share is used as evidence for concluding that the two things are similar in other respects.
It is an argument that depends on a comparison of instances. Simple arguments from analogy have the following structure :

Entity A has attributes a, b, c, and z
Entity B has attributes a, b, c.
Therefore, entity B probably has attribute z also.

Evaluating Analogical Arguments
The stronger the connection between the things compared, the more likely the conclusion is; the weaker the connection, the less likely the conclusion.
Four factors affects the strength of analogies :
(1) Number of Entities Involved
Ordinarily, the more instances lying at the base of the analogy, the greater the livelihood of it conclusion.
The more Volkswagens that performed well, the stronger the analogical argument that this new car probably would be dependable.
(2) Number of Relevant likenesses
The more relevant likenesses among the instances, the stronger the analogical argument and more likely its conclusion. For e.g., they have the same model.
(3) Number of Differences
The more strengthening differences between the things compared, the stronger the analogical argument itself. For eg., other different drivers found that car dependable.
The more weakening differences, the weaker the analogical argument. For eg., Peter drives mostly on the highway but John does mostly city driving.
(4) Strength of the Conclusion Relative to the Premises
This criterion is the same on the margin for error applied to inductive goveralizations. The stranger the conclusion, the weaker the analogical argument [and the less likely its conclusion]. In other words, the more specific the conclusion is, the easser the argument is to be falsify. For eg., Peter had average 27 miles per gallon with his VW Rabbits the argument is strong, if John conclude that he would average over 20 mrg.




















Causal Arguments : Cause & Effect

Some inductive arguments aim to establish the causes of different kinds of things and events. These causal arguments attempt to support the causal propositions, for instance, “Penicillin can cure syphilis”.

A cause is the condition for bringing about a thing or event.

A necessary condition for occurrence of a specified event is a circumstance in whose absence the event cannot occur. For eg., the presence of oxygen is the inevitable cause of the lighting of a match.

A sufficient condition for occurrence of a specified event is a circumstance in whose presence the event must occur. For eg., being guillotined is a sufficient cause of death.

A necessary and sufficient condition is a circumstance that must be present for the effect to occur and that will bring about the effect alone and of itself. For eg., an increase in voltage cause an increase in electrical current. For an electrical current to increase through a resistive circuit, nothing more and nothing less is required than an increase in voltage.

Mill’s Methods
In formulating and evaluating causal arguments, we must judge whether the evidence establishes a relationship between a phenomenon and an alleged cause. Mill’s five methods are proposed for establishing causal relationships.

The Method of Agreement

If two or more instances of a phenomenon have only one circumstance in common, that circumstance is probably the cause (or the effect) of the phenomenon.

A B C D occur together with W x y z.
A E F G occur together with W t u v
Therefore, A is the cause (or the effect) of W.

Instance Antecedent Circumstance Phenomenon
1 A B C E F S
2 A B D E S
3 A C D F S

Therefore, A is the cause (or the effect) of S.

Example : Three students go on a picnic. In the evening all students have got a stomachache. We guess that the causes should be foods, so we collect the data of foods consumed during that day. We have foods marked by A, B, C, D, E and F.

Student 1 A B C E F Stomachache
Student 2 A B D E Stomachache
Student 3 B C D F Stomachache

We conclude the table that Ford – B causes the stomachache.

The Method of Difference

If a circumstance is present in an instance when the phenomenon is present and absent in an instance when the phenomenon is absent, and the two instances are alike in every other expect, then that circumstance is probably the cause (or the effect) of the phenomenon.

A B C D occur together with W X Y Z.
- B C D occur together with - X Y Z.

Therefore, A is the cause C or the effect, of W.
Instance Antecedent Circumstance Phenomenon

1 A B C D E F S
2. A B C D E - -

Therefore, F is the cause (or the effect) of S.

Joint Method of Agreement and Difference
The use of both methods affords a higher probability to the conclusion.

A B C --- x u z A B C ---- x y z.
A D E --- x t z B C ---- y z.

Therefore, A is the effect (or the cause) of x.
Take the example concerning the discovery of the identity of the leaked of confidential information.

John’s Cohen’s Smith’s Leaked to
Access Access Access press

Agree.1 absent present present present
2 absent present present present
Diff.3 present absent present present
4 present absent absent present
Smith is the cause of the leaks.



The Method of Residues

The method of residues consists of separating from a group of causally connected conditions and phenomena those strands of causal connection that are already known, learning the required causal connection as the “residue”.

A B C --- x y z
B is known to be the cause of y.
C is known to be the cause of z.

Therefore, A is the cause of x.

Example :
Student A is absent and is the cause of x which is not the robbery.
Student B is ill and is the cause of y which is not the robbery.
So : Student C is the cause of robbery.

The Method of Concomitant Variation
If a given phenomenon varies I amount or degree in some regular way with the amount or degree of some other phenomenon, then the two factors are causally related.

A B C X Y Z A X
A + B C X + Y Z A + X –
A – B C X – Y Z A – X +


Therefore, A and X are causally connected.
For eg., because those who smoke more cigarettes get lung cancer more often, we conclude that cigarette smoking is causally related to death by lung cancer. And as the blood pressure increases and decreases, so does the intensity of the brain waves; the doctors conclude that the two conditions are causally related.

Fallacies
A fallacy is an error in reasoning. It is a way that an argument can fail to establish the truth of its conclusion; i.e. its premises do not support its conclusion.
A fallacy is a certain kind of defect in an argument. One way that an argument can be defective is by having one or more false premises. Another way is by containing a fallacy. Both deductive and inductive arguments may be affected by fallacies.

1. Fallacies of Presumption
These fallacies arise because the premises presume what they
purport to prove.
Begging the Question (Petitio Principii)
Begging the question arises when an argument fails to prove
anything because it somehow talus for granted what it is supposed to prove.
Ex. Johnes is demented; therefore he is insane.
The premise of this argument is merely another proposition of the conclusion because “demented” and “insane” have the same meaning.

Complex Question
The fallacy of complex question occurs when an arguer uses a
question that presupposes the truth of some conclusion suried in that question in order to get a desired conclusion. This fallacy attempt to trick the respondent into making some statement that will establish the truth of the presumption hidden in the question.

Ex. “Have you stopped beating your wife yet?
If your answer is “Yes”, it follows that you have beated in the past.
If your answer is “No”, it follows that you continue to beat.

2. Fallacies of Ambiguity
These fallacies arise from the occurrence of some form of ambiguity
in either the premise or the conclusion or both.

2.1 Equivocation
The fallacy of equivocation occurs when the conclusion of an
argument depends on the fact that on or once words are used, cither explicitly or implicitly, in two different senses in the argument.

Ex. Any law can be repealed by the legislative authority. But the
law of gravity is a law. Therefore, the law of gravity can be repealed by the legislative authority.

2.2 Amphiboly
The fallacy of amphiboly occurs in arguing from premises whose formulations are ambiguous because of their grammatical construction.

Ex. John told Henry that he had made a mistake. It follows that John has at least the courage to admit his own mistakes.
In this argument the pronoun “he” has an ambiguous antecedent; it can refer either to John or to Henry.

2.3 Composition
The fallacy of composition occurs when it is argued that because the parts have a certain attribute, it follows that the whole has that attribute too and the situation is such that the attribute in question cannot be legitimately transferred from parts to whole.
Ex. Each player on this basketball team is an excellent athlete.
Therefore, the team as a whole is excellent.

Each atom in this piece of chalk is invisible.
Therefore, the chalk is invisible.
Not every such transference is illegitimate, however, consider the following arguments:
Every atom in this piece of chalk has mass. Therefore, the piece of chalk has mass.
Every picket in this picket fence is white. Therefore, the whole fence is white.

In each case an attribute (having mass, being white) is transferred from the parts onto the whole, but these transferences are quite legitimate. Indeed, the fact that the atoms have mass is the very season why the chalk has mass. The same reasoning extends to the fence.

2.4 Division
The fallacy of division is the exact reverse of composition. The fallacy occurs when the conclusion of an argument depends on the erroneous transference of an attribute from a whole (or a class) onto its parts (or members).
Ex. Since a certain corporation is very important and Mr. Doe is an official of that corporation, therefore Mr. Doe is very important.
Like composition, however, this kind of transference is not always illegitimate. The following argument contains no fallacy:
This piece of chalk has mass. Therefore, the atoms that compose this piece of chalk have mass.

3. Fallacies of Relevance

A fallacy of relevance occurs when an argument relies on premises that are not relevant to its conclusion.

Appeal to Ignorance
An argument commits an appeal to ignorance when it is argued that
a proposition is true simply on the basis that it has not been proved false, or that it is false because it has not been proved true.

Ex. People have been trying for centuries to provide conclusive
evidence for the claims of astrology, and no one has ever succeeded. Therefore, we must conclude that astrology is lot of nonsense.

Conversely, the following argument commits the same fallacy.
People have been trying for centuries to disprove the claims of astrology, and no one has ever succeeded. Therefore, we must conclude that the claims of astrology are true.

False Cause
The fallacy of false cause occurs when an argument relies on treating as
the cause of a thing what is not really its cause. A variety of false cause is widely called the fallacy of pos hoc ergo propter hoc (“after the thing, therefore because of the thing”). Ex :

During the past two months, every time that the cheerleaders have worn blue ribbons in their hair, the basketball team has been defeated. Therefore, to prevent defeats in the future, the cheerleaders should get rid of those blue ribbons.

Argument Against the Person
(Argumentum ad Hominem)

An argument is ad hominem if it is directed at an opponent in a controversy rather than being directly relevant to proving the conclusion under discussion.
This argument occurs in three forms :

3.3.1 ad hominem abusive In this form, it attacks the opponent instead of offering direct reasons why his views are incorrect. Ex :

“Karl Marx must have been mistaken in maintaining that capitalism is an evil form of economic and social organization. Why, he was a miserable failure of a man who couldn’t even earn enough money to support his family.”

3.3.2 ad hominem circumstantial
This form occurs if a speaker attempts to discredit the opponent’s argument by alluding to certain circumstances that affect the opponent. The speaker hopes to show that the opponent is predisposed to argue the way he or she does and should therefore not be taken seriously. Here is an example :
Lee Iacocca has argued that cars manufactured by Chrysler are of higher quality than equally priced Japanese cars. But given that Iacocca is chairman of the Chrysler Corporation, he would naturally be expected to argue this way. Therefore, Iacocca’s argument should be ignored.

3.3.3 The tu quoque
The tu quoque (“You too”) fallacy occurs when an arguer, trying to show that he is not fault, argues that his opponent has said or done things just as bad as those of which he, the arguer, is accused. Ex :

A child replies to his parent : Your argument that I should stop tealing candy from the corner store is no good. You told me yourself just a week ago that you, too, stole candy when you were a kid.

Not all ad hominem arguments are fallacious, however. They can be good arguments or they can be of some value, though never as a direct proof of the conclusion.